Einstein Ring

An Einstein ring is the image produced by gravitational lensing when a background source, a foreground lensing mass, and the observer are perfectly aligned. By the rotational symmetry of the configuration, light from the source reaches the observer along every azimuth around the lens, and the two images of a generic lens merge into a single luminous circle. The ring's angular radius is the Einstein radius θ_E = √(4GM/c² · D_LS/(D_L D_S)), which depends on the lens mass and on the observer–lens, observer–source, and lens–source distances.

The Einstein radius is the natural angular scale of any lens. For one star lensing another it is only a few milliarcseconds — far too small to resolve, which is why Einstein himself, calculating the ring in 1936, judged that 'there is no hope of observing this phenomenon directly.' He had in mind stellar lenses. For a galaxy lensing a galaxy, θ_E is of order an arcsecond and easily resolved, and dozens of such rings have now been imaged by the Hubble and James Webb space telescopes as glowing circles wrapped around foreground elliptical galaxies.

When alignment is imperfect the ring breaks into arcs or into the standard pair of images of a point lens; a partial Einstein ring — an arc spanning part of the circle — is the more common observed form. Because the ring's radius encodes the enclosed lens mass directly, a measured Einstein ring is a precise scale for weighing galaxies, including the dark matter they contain.

The ring geometry was first worked out by Orest Khvolson in 1924 and independently by Einstein in a 1936 Science note prompted by the amateur Rudi Mandl. The first ring was imaged in the radio source MG1131+0456 in 1988; optical and infrared rings became routine with the Hubble Space Telescope.